Abstract— Beamforming based on microphone array is a method to identifysound sources. It can visualize the sound field of the source plane and revealinteresting acoustic information. This paper represents a tutorial offundamental array of processing and beamforming theory releavant to microphonearrays. Microphone arrays have great potential in practical applications ofspeech processing operations.
I. INTRODUCTION Array processing involves the useof multiple sensors to receive or transmit a signal carried by propagatingwaves. Sensor arrays have applications in a diversity of fields such as sonar, defense industry, seismology,astronomy, tomography, smart home systems etc. In this paper we are going toshed some light on microphone arrays which are used to receive acousticsignals, or more specifically speech signals. then we are going to examine atechnique called “Beamforming”. Starting from the invention oftelephone systems in the late 19th century, sound signal acquisition has beenan essential part of speech processing.
Most early sound acquisition systemsuse only a single microphone but such systems were not found to be very good.In challenging acoustic environments where there are noise, echo, reverberationand interferences. For a better control of the mentioned problems andpreservation of the spatial sound realism, multiple microphone systems wereinvented. In the literature, microphonearrays are generally classified into two major categories: additive anddifferential. First one refers to arrays with large sensor spacing whoseoutputs are responsive to the acoustic pressure field. Whereas the second one refersto arrays with small sensor spacing whose outputs are responsive to the differentialacoustic pressure field of different orders. Both types of arrays have theirown pros and cons and they will be investigated later on.
A microphone array systemconsists of two important components; a hardware and an algorithm. Theselection of sensors, amplifiers and multichannel convertors are out of ourscope. For the latter, a large variety of processing algorithms have beenstudied in the literature in order to enhance certain signals or signalcomponents from the microphones’ output. e.g: channel identification, channelequalization, multichannel noise reduction, blind source separation andbeamforming. Beamforming is a technique usedto process microphone array data in order to find the direction of incidentacoustic waves and estimate the power of sound source1. Beamforming consistsof designing a spatial filter that can take advantage of the spatiotemporalinformation embedded in the microphone array outputs to form a response withdifferent sensitivities to sounds arriving from different directions.
Research in microphone arraybeamforming started in the late 1960s although some of the fundamentalprinciples can be traced back to the 1930s when directional microphones were invented.2Early works in this area were strongly influenced by the sensor array theorydeveloped in the field of radar and sonar. Beamforming techniques can bebroadly classified as being either data-independent or data-dependent.Data-independent or fixed beamformers are so named because their parameters arefixed during operation.
However data-dependent or adaptive beamformingtechniques continuously update their parameters based on the received signals.Next chapter will explain a summary of beamforming techniques, indicating theiradvantages and disadvantages.II. Beamform?ng TypesA. Delay-sum Beamforming The simplest of all microphonearray beamforming technique is delay-sum beamforming. Delay-sum beamforming isso-named because the time domain sensor inputs are first delayed by ?nseconds, and then summed to give a single array output. Usually, each channelis given an equal amplitude weighting in the summation so that the directivitypattern demonstrates unity gain in the desired direction.
B. Filter-sum Beamforming The delay-sum beamformer belongsto a more general class known as filter sum beamformers, in which both theamplitude and phase weights are frequency dependent. In practice, mostbeamformers are a class of filter-sum beamformers.C. Subarray Beamforming The dependency on the operatingfrequency means that the response characteristics(beam-width, sidelobe level)will only remain constant for narrow-band signals where the bandwidth is not asignificant proportion of the centre frequency. However speech is a broad-bandsignal meaning that a single linear array design is inadequate if a frequencyinvariant beam-pattern is desired. One simple method is to implement the arrayas a series of subarrays. These subarrays are designed to give desired responsecharacteristics for a given frequency range.
The subarrays are generallyimplemented in a nested fashion such that any given sensor may be used in morethan one subarray. Each subarray is restricted to a different frequency rangeby applying band-pass filters. An illustration of a design covering 4 differentfrequency bands is shown in Figure 1. Figure1: Sample nested subarraystructure D.Superdirective Beamforming Conventional linear arrays with sensors spaced at ?/2have directivity that is approximately proportional to the number of sensors,N.
It has been found that the directivity of linear endfire arraystheoretically approaches N2 as the spacing approaches zero in adiffuse noise field. Beamforming techniques that use this capability forclosely spaced endfire arrays are termed superdirective beamformers. For speechprocessing applications, superdirective methods are useful for obtainingacceptable array performance at low frequencies for realistic array dimensions.The wavelength for acoustic waves at 500 Hz is approximately 0.66 m and that iswhy sensor elements spaced closer than 0.
33m in an endfire configuration can beused in the low frequency range to improve performance.E.Near-field Superdirective Beamforming Low frequency performance isproblematic for conventional beamforming techniques because large wavelengthsgive negligible phase differences between closely spaced sensors, leading topoor directive discrimination. Tager3 states that delay weight sumbeamformers can roughly cover the octave band before excessive loss ofdirectivity occurs. A frequency of 100 Hz corresponds to a wavelength of 3.
4mthis would give an array dimension of 3.4m < L < 6.8m which isimpractical for many applications.
One such method is a techniquepropes by Tager4 called near-field superdirectivity. This is due to the factthat it takes the amplitude differences into accounts as well as the phasedifferences. While the phase differences are negligible at low frequencies, the amplitude differences are significant.Particularly when the sensors are placed in an endfire configuration as thismaximises the difference in the distance from the source to each microphone.F. Generalised Sidelobe Canceler (GSC)The most famous adaptive beamformingtechnique that addresses this limitation is derived from Frost5. Frost’salgorithm belongs to a class of beamformers known as linearly constrainedminimum variance (LCMV) beamformers. Perhaps the most commonly used LCMVbeamforming technique is the generalised sidelobe canceler (GSC)6.
Itseperates the adaptive beamformer into two main processing paths. The firts ofthese implements a standard fixed beamformer, with constraints on the desiredsignal. The second path is the adaptive portion which provides a set of filtersthat adaptively minimise the power in the output.III. Overview of Beamforming Techniques This section summarises theimportant characteristics of the beamforming techniques discussed in previoschapter. Table 1 indicates wheter or not it is a fixed or adaptive techniqe,optimal noise conditions for its use and its optimal array configuration.
Table2 indicates advantages and disadvantages of the techniques.TABLE I. Properties of beamformingtechn?ques Technique Fixed/Adaptive Noise Condition Array Conf.
Delay-sum Fixed Incoherent Broadside Subarray Fixed Incoherent Broadside Superdirective Fixed Diffuse Endfire Near-field Fixed Diffuse Endfire GSC Adaptive Coherent Broadside TABLE II. advantages/d?sadvantages ofbeamform?ng tech. Technique Advantages Disadvantages Delay-sum Simplicity Low frequency performance, narrow band Subarray Broadband Low frequency performance Superdirective Optimised array gain Assumes diffuse noise Near-field Optimised array gain, near field sources, low frequency performance Assumes diffuse noise, assumes noise in far-field GSC Adapts to noise conditions, minimises output noise power Low frequency performance, can distort in practice AcknowledgmentThis work was supported by mechanical engineering department ofHacettepe University. References1 S.Haykin,Array Signal Processing. Prentice Hall, 1985.
2 Chen J,Benesty J, Pan C, On the Design and Implementation of Linear DifferentialMicrophone Arrays, J Acoust Soc Am, 136:3097-31133 W.Tager,Near Field Superdirectivity(NFSD) in Proceedings of ICASSP, pp. 2045-2048, 19984 W.Tager,Etudes en Traitement d’Antenne pour la Prise de Son, PhD thesis, Universite deRennes, 1998. 5 O.
L.Frost, An Algorith for Linearly Constrained Adaptive Array Processing,Proceedings of the IEEE, vol. 60, pp. 926-935, August 1972.6 L.Griffiths and C.
Jim, An Alternative Approach to Linearly Constrained AdaptiveBeamforming IEEE Trans. on Antennas and Propagation, vol. 30(1), pp.27-34,Jamuary 1982.